Take a look at 47 + 38. No pencil, no paper, no column method. Could you work it out in your head?
There's more than one way to do it. Today we'll look at three of them, and by the end of the lesson you'll be able to pick the one that best suits the numbers in front of you.
Write 47 + 38 in large numerals on the IWB and give the class five seconds of quiet think-time before any hands go up. Take three or four answers and ask 'how did you do it?' rather than 'what's the answer?'. Park each method on the board without judging it; pupils will see the same answer arrive three different ways in the next step.
Watch four worked examples on the number line. Same answer every time, but the route across the line is different. Notice how each strategy uses the numbers in a slightly different way.
Split the 38 into 30 + 8. Jump +30 first to land on 77, then jump +8 to land on 85.
40 is friendlier than 38. Jump +40 to land on 87, then take back the extra 2 to land on 85.
50 is the friendliest landing place near 47. Jump +3 to land on 50, then jump +35 in one go to land on 85.
198 is almost 200. Jump +200 to land on 435, then take back the extra 2 to land on 433. Compensating shines when one number is just below a round hundred.
Walk each example one at a time. Point at the start, the arc, the landing point, and the strategy label as you say each step aloud. Pacing target: about two minutes each on Examples 1, 2 and 3, and about three minutes on Example 4 so the why-the-numbers-decide point lands properly. If you find yourself still on Example 1 after three minutes, move on — the routes repeat the same idea and each one buys back time.
Today's problem: 38 + 27. Three pupils in turn will come to the board — one for each strategy — and drag the jump arcs onto the number line to reach the answer. The strategy-hint label confirms which one they used.
While one pupil drags at the board, watch the route take shape and think about which strategy it is — partition, compensate, or bridge.
This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.
Call up three pupils in turn — one for each strategy — so the class sees all three routes to 65. After each route lands, ask 'which strategy did you choose, and why?'
Pacing break between turns. Before calling the next pupil up, give the class a few seconds of silent think — which strategy would you reach for next, and why? — then take one pupil's answer before calling the next up.
If a pupil draws an arc that doesn't reach 65, do not correct on their behalf — ask the rest of the class to spot the error.
In your maths copy, work each mental example three ways — partition, compensate, and bridge — so you can decide which strategy fits which numbers best.
For each problem below, set up three short lines underneath it. Label each line with the strategy and write the two jumps you took. Use these examples:
At the end, circle the strategy on each problem that you found cleanest for those numbers.
Two problems, three strategies each — six labelled mini-solutions in six minutes. That is the right pace for Stage 4 pupils to actually finish without rushing. Walk the row glancing at the labels and the jump sizes — this is whole-class copybook practice, not marking. Look for two things: the take-back jump being the right size in compensating, and the bridge jump landing on a round number. If you spot a pupil writing the same numbers under all three strategies, prompt them quietly to redo the compensate row with a back-jump.
235 + 198 is the headline example here — it is where compensating becomes obviously the right tool and partitioning becomes obviously three jumps. Make sure pupils reach it; if a row is still on 47 + 38 at the four-minute mark, nudge them on.
Today's bank: four rounds of fact-race, building from bonds to 20 right through to bonds to 1000. These are the friendly numbers your mental strategies will lean on for the rest of the year — speed and accuracy both count.
One pupil at a time comes to the board to type the missing number. While they type, the rest of the class works out the answer too, then we check it together once it's on the board.
This round is the practice bank — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.
Run one round at a time. Read the first question aloud, then nominate a pupil to come to the board and type the missing number. Take the class's answer, confirm it, bank the time score, and move to the next round.
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